Systems of advance-delay differential-difference equations and transformation groups

• Main Authors: Serguei I. Iakovlev, Valentina Iakovleva
• Format: Article
• Language: English
• Published: Texas State University 2016-12-01
• Series: Electronic Journal of Differential Equations
• Subjects: Advance-delay differential-difference equations; step derivation method; uniqueness; transformation group; infinitesimal generator; point spectrum
• Online Access: http://ejde.math.txstate.edu/Volumes/2016/311/abstr.html

A linear system of mixed-type differential difference equations is studied. A step derivation method and some conditions on an initial function are used to guarantee existence, uniqueness and smoothness of the solution. Further, a transformation group is defined on a complete countably normed space of initial functions and the spectrum of the infinitesimal generator of this group is studied. The same technique applies to a linear system of retarded differential difference equations. A problem to extend solutions of such a system to the left on the real line is solved.